Multidimensional Analysis Of Preference Research Articles

Multiple criteria group decision analysis using a Pythagorean fuzzy programming model for multidimensional analysis of preference based on novel distance measures

The preference concerning criteria or alternatives from decision makers (DMs) is a critical element in multicriteria group decision making (MCGDM). The linear programming technique for the multidimensional analysis of preference (LINMAP) is the most influential technique in adjusting the error between the objective assessments on criteria and subjective preferences on alternatives via optimal programming for MCGDM problems. Considering the higher capacity for expressing the uncertainties of human inherent preferences of the Pythagorean fuzzy (PF) sets, this article explores the LINMAP technique for MCGDM problems under the PF scenario. First, we present a novel (squared) Euclidean distance measure for the PF sets since it possesses captivating characteristics of the PF sets and the distance measure. Second, we define the preference degrees over alternatives that are expressed as PF sets and calculate their magnitudes via relative distances, which are used to calculate the consistency and inconsistency indices. Third, the ordered weighted averaging (OWA) operator under the normal distribution is introduced to obtain the weights of DMs to reduce the influence of unfair arguments. Fourth, we construct the biobjective PF-LINMAP model for minimizing both the error extents and the overall distances to the PF positive ideal solution for the minimum error and global optimum. Then, we obtain the optimal criterion weights and ranks of the candidates via relative closeness indices. Finally, we perform our PF-LINMAP method to choose the optimal green supplier, and we implement the sensitivity analysis and comparative analysis with those of the available PF-LINMAP methods to verify the feasibility and superiority of our approach.

A GENERAL MULTI-ATTRIBUTE MULTI-SCALE DECISION MAKING METHOD BASED ON DYNAMIC LINMAP FOR PROPERTY PERCEIVED SERVICE QUALITY EVALUATION

The scientific evaluation of property perceived service quality (PPSQ) needs multi-stage, multi-source and large-group perceived information, which is deemed to be the decision problem for dynamic, heterogeneous and large-scale data processing. Aiming at the problem, we propose a general multi-attribute multi-scale (MAMS) method based on the dynamic linear programming technique for multi-dimensional analysis of preference (LINMAP). In the dynamic LINMAP model, the classic MAMS matrix is introduced and extended into a general form. The dynamic LINMAP model is constructed by defining dynamic consistency and dynamic inconsistency. The time series weight is determined by Orness method. The new method adapts to the requirements of modern PPSQ. Finally, we verify the feasibility and effectiveness of dynamic LINMAP method by analyzing a PPSQ evaluation example. The new method improves the traditional PPSQ evaluation, and provides a perspective for large-scale data processing by the classic decision method.

Optimal design parameters and performance optimization of thermodynamically balanced dish/Stirling concentrated solar power system using multi-objective particle swarm optimization

In this work, a theoretical model based on opto-geometric and thermodynamic analyses of Solar Dish-Stirling System (SDSS) considering opto-geometric sizing criteria and energy balance of different system components has been developed. An optimization algorithm has been also implemented for simultaneously maximizing the output power and total efficiency of the SDSS using the Multi-Objective Particle Swarm Optimization (MOPSO). Nine decision variables have been considered, namely, the interception factor, mirror reflectance of the concentrator, receiver absorbance, receiver transmittance, receiver emissivity, tilt angle of the receiver, the direct solar intensity, the speed of wind, and the temperature of ambient. Pareto optimal frontier (POF) was determined and the optimal solution was selected by applying a decision making approach called the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). Moreover, a sensitivity analysis was also carried out to identify the impact of the rim angle, the dish concentrator diameter, the mirror soiling coefficient of concentrator, and the ratio of design concentration on the SDSS performance optimization. The results showed that the proposed MOPSO shows a feasible approach to achieve a maximal power output of 23.46 kW with an optimal final total efficiency of 30.15% that approaches the ideal solution. Moreover, the sensitivity results indicated that SDSS with concentrator diameters of (2.5–15 m) can produce final optimal output powers of (1.43–53.34 kW) with insignificant variation in the overall efficiency (29.80–30.20%), at the obtained optimal solutions for the optimized dish concentrator configurations. Moreover, the results also emphasize how mirror soiling factor of the concentrator, has a dramatic effect on the optimal electric power and total efficiency of SDSS. It can be concluded that the proposed MOPSO approach can lead to more desired results and allow the technical feasibility for design of SDSS according to the need of such output power required for a certain application.

Cognitive fuzzy sets for decision making

The intuitionistic fuzzy set (IFS) is useful in information expression but the cognitive overlap of people might cause the situation where the membership degree plus non-membership degree is greater than 1. The linear programming techniques for multidimensional analysis of preference (LINMAP) method is a well-known decision-making approach but little research focused on the interactive multiple criteria decision making (MCDM) problems within the LINMAP framework. This paper aims to propose a cognitive fuzzy set (CFS) to overcome the drawbacks of IFSs, and then develop an interactive cognitive fuzzy LINMAP (CF-LINMAP) method. To achieve these goals, the joint degree, which is caused by the cognitive overlap, of an IFS is interpreted, and then the concept of the CFS is proposed. We define the distance measure and comparison of CFSs, based on which, the cognitive fuzzy consistency and inconsistency indexes are calculated. The irrational index, which represents the irrational degree of experts, is introduced to improve the consistency and inconsistency indexes at each decision-making stage. Afterwards, an interactive CF-LINMAP method is proposed to deal with MCDM problems. An illustration concerning the hospital internal supply chain selection is given to show the applicability of the interactive CF-LINMAP method. Finally, the sensitivity analysis is done to demonstrate the reliability of the results.

A Novel Three-Phase LINMAP Method for Hybrid Multi-Criteria Group Decision Making With Dual Hesitant Fuzzy Truth Degrees

Based on the idea of linear programming technique for multidimensional analysis of preference (LINMAP), a novel three-phase LINMAP method is presented here for solving hybrid multi-criteria group decision making (MCGDM) with dual hesitant fuzzy (DHF) truth degrees and incomplete criteria weights information. Firstly, by simultaneously taking into account the difference between each alternative and all the others for the decision maker (DM), the difference of each alternative between the individual DM and the decision group, and the difference of each alternative between the individual DM and all the others, a tri-objective nonlinear programming model is created to determine the DMs' weights. Secondly, to derive the criteria weights, objective positive ideal solution (OPIS), and the objective negative ideal solution (ONIS), a new four-objective DHF mathematical programming model is established by minimizing inconsistency and maximizing consistency based on OPIS and ONIS, and a pair of parametric nonlinear programming models are technically established by unequal weighted summation approach for solving the four-objective DHF mathematical programming model, which can provide DMs with more agility and flexible space to change their preference. Thirdly, by considering the distances of each alternative from the OPIS and ONIS for individual DM and the decision group, a minimizing deviation optimal model is established to derive the group ranking order of alternatives. Finally, a new method is put forward for solving hybrid MCGDM with DHF truth degrees, and the validity and practicability of the proposed method is analyzed through a case of water quality monitoring system (WQMS) selection.

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

This paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker’s preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.

Towards an Adaptive Design of Quality, Productivity and Economic Aspects When Machining AISI 4340 Steel With Wiper Inserts

The continuous pursue of sustainable manufacturing is motivating the utilization of new advanced technology, especially for hard to cut materials. In this study, an adaptive approach for optimization of machining process of AISI 4340 using wiper inserts is proposed. This approach is based on advance yet intuitive modeling and optimization techniques. The approach is based on Artificial Neural Network (ANN), Multi-Objective Genetic Algorithm (MOGA), as well as Linear Programming Techniques for Multidimensional Analysis of Preference (LINMAP), for modeling, optimization and multi-criteria decision making respectively. This integrated approach, to best of the authors’ knowledge, has been deployed for the first time to adaptively serve different designs of manufacturing processes. Such designs have different orientations, namely cost, quality, productivity, and balanced orientation. The capability of the proposed approach to serving such diverse requirements answers one of the most accelerating demands in the manufacturing community due to the dynamics of the uprising smart production lines. Besides, the proposed approach is presented in a straightforward manner that can be extended easily to other design orientations as well as other engineering applications. Based on the proposed design, a balanced general setting of 197.4 m/min, 0.95 mm, and 0.168 mm/rev was recommended along with other settings for more sophisticated requirements. Confirmatory experiments showed a good agreement (i.e., no more than 7% deviation) with the predicted optimum responses. This shows the validity of the proposed approach as a viable tool for designers to promote holistic and sustainable process design.

Thermodynamic Assessment and Multi-Objective Optimization of Performance of Irreversible Dual-Miller Cycle

In this study, a new series of assessments and evaluations of the Dual-Miller cycle is performed. Furthermore, the specified output power and the thermal performance associated with the engine are determined. Besides, multi-objective optimization of thermal efficiency, ecological coefficient of performance (ECOP) and ecological function ( E u n ) by means of NSGA-II technique and thermodynamic analysis are presented. The Pareto optimal frontier obtaining the best optimum solution is identified by fuzzy Bellman-Zadeh, Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) decision-making techniques. Based on the results, performances of dual-Miller cycles and their optimization are improved. For the results of the condition that (n < k) the best point has been LINMAP answer. The thermal efficiency for this point has been 0.5388. In addition, ECOP and E u n have been 1.6899 and 279.221, respectively. For the results of the condition that (n > k) the best point has been LINMAP and TOPSIS answer. The thermal efficiency for this point has been 0.5385. Also, ECOP and E u n have been 1.6875 and 279.7315, respectively. Furthermore, the errors are examined through comparison of the average and maximum errors of the two scenarios.

A Hybrid Model of Multi-Objective Differential Evolution Algorithm and Various Decision-making Methods to Optimize the Batch ABE Fermentation Process

In recent years, biofuels have attracted considerable attention as renewable and clean source of energy and have been playing the role of suitable alternatives to fossil fuels. One of the most attractive types of biofuels is Acetone-Butanol-Ethanol (ABE) which is produced in a batch fermentation process by the anaerobic bacterium Clostridium acetobutylicum and sugar-based substrate as feedstock. In this paper, optimization of this process was carried out according to a bi-objective function. A hybrid model of Multi-Objective Differential Evolution (MODE) algorithm and distinguished decision-making methods, namely Linear programming technique for Multidimensional Analysis of Preference (LINMAP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Shannon's entropy were applied to find the final optimal operating point. The initial concentration of substrate and the final operating time of the process were selected as decision variables to maximize two main objectives in terms of solvents yield and productivity. A Pareto optimal set presents a wide range of optimal operating points and a proper operating condition can be selected based on the necessities of the applicant. The best optimal point obtained by TOPSIS, according to the lowest value of deviation index, was also compared with the results of economic-based optimization.

Multi-objective optimization of solar powered adsorption chiller combined with river water heat pump system for air conditioning and space heating application

Multi-energy system is currently under rapid development due to their potential to reduce the use of fossil fuel resources and improve system stability. A systematic simulation-based, multi-objective optimization model of for solar hybrid heat pump heating and cooling system is presented. A combined energy, economic and environmental analysis of the system is conducted to calculate the primary energy use as well as the levelized total annual cost. A multi-objective optimization model is formulated using a genetic algorithm to simultaneously minimize these objective. Linear programming technique for multidimensional analysis of preference (LINMAP) is used to select the optimal point from the Pareto front. A sensitivity analysis is also performed to assess the influence of fuel cost, capital cost of innovative components and the annual interest rate on the Pareto front of the optimal solution.

Thermodynamic, economic and environmental impact studies on various distillation units integrated with gasification-based multi-generation system: Comparative study and optimization

Abstract This research proposes four scenarios for a multi-generation system to produce power, pasteurized milk, biofuel and fresh water for the northern areas of Iran. In all scenarios, power, pasteurized milk and biofuel are produced by a similar arrangement of a supercritical CO2 (S–CO2) Brayton cycle, a biomass gasifier and a milk pasteurization unit while the portable water is produced by a brine recirculation multi-stage flash (BR-MSF) in scenario 1, by forward, backward and parallel feed schemes of multi-effect distillation (BF, FF and PF-MED) in scenarios 2, 3 and 4, respectively. A comparative study is conducted for the exergy, exergoeconomic and exergoenvironmental performances of all scenarios with various stages and effects using Engineering Equation Software (EES). The optimum performances of all scenarios are found by applying the fast and elitist non-dominated sorting genetic algorithm (NSGA-II) and using linear programming technique for multi-dimensional analysis of preference (LINMAP), technique for order of preference by similarity to ideal solution (TOPSIS) and Shannon entropy decision makers. According to the results, the maximum distillate water with capacity of 400.6 m3/day is obtained for scenario 1 through Shannon entropy method. Moreover, scenario 4 gives the maximum exergy efficiency with a value of 44.16% using LINMAP method and scenario 2 with the lowest total cost and environmental impact (EI) rates of 77.15 $/h and 33.35 mPts/s, respectively obtained from TOPSIS method is the best layout from the economic and EI aspects.

Multi-objective optimization design of spur gear based on NSGA-II and decision making

Optimization design of spur gear is a complicated work because the performance characteristics depend on different types of decision variables and objectives. Traditional single-objective optimization design of the spur gear always results in poor outcomes relative to other objectives due to objectives’ competition with each other. Therefore, this study works on the spur gear design based on the multi-objective optimization model of elitist non-dominated sorting genetic algorithm (NSGA-II). In the model, gear module, teeth number, and transmission ratio are decision variables, while center distance, bearing capacity coefficient, and meshing efficiency are objectives. Final optimal solutions are picked out from Pareto frontier calculated from NSGA-II using the decision makers of Shannon Entropy, linear programming technique for multidimensional analysis of preference (LINMAP), and technique of order preference by similarity to an ideal solution (TOPSIS). Meanwhile, a deviation index is used to evaluate the reasonable status of the optimal solutions. From triple-objective and dual-objective optimization results, it is found that the optimal solution selected from LINMAP decision maker shows a relatively small deviation index. It indicates that LINMAP decision maker may yield better optimal solution. This study could provide some beneficial information for spur design.

A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets

Multiple criteria decision making (MCDM) approach plays an important role in life, since it is always necessary to make decisions through various alternatives based on specific criteria. In this paper, interval type-2 fuzzy sets (IT2FSs) are used because in most cases in the real-world the information is incomplete and ambiguous. A new group decision approach with linear assignment method (LAM) is proposed. In addition, weight of each evaluation factor according to subjective and objective data is constructed based on a new developed version of linear programming technique for multidimensional analysis of preference (LINMAP) method. In the proposed method, weights of decision makers (DMs) are computed based on a novel approach that applies a new modified method based on the concept of ideal solutions. Furthermore, a new IT2F-ranking method is introduced. To display the applicability of the presented soft computing method, firstly, a real case study of green supplier selection problem is adopted from the literature and solved. Moreover, the method is applied in a second case study of project evaluation and selection problem. Two applications show that the introduced method presents a proper soft computing framework that can handle real-world uncertain environments. Moreover, the method can consider importance of the DMs and evaluation criteria.

Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness

This paper aims to utilize the core structure of linear programming technique for multidimensional analysis of preference (LINMAP) to propose a parametric LINMAP methodology for addressing multiple criteria group decision-making problems based on Pythagorean fuzzy sets. To compare Pythagorean membership grades, this paper presents a Hamming distance-based approach for identifying closeness-based order relations based on Pythagorean fuzzy closeness indices. The concept of comprehensive closeness measures is introduced to measure individual order consistency and inconsistency between subjective preference relations and objective order relations. In the spirit of LINMAP, this paper determines individual goodness of fit and poorness of fit and further constructs a novel parametric LINMAP model. The applicability of the developed approach is explored by a practical application of railway project investment. Some comparative analyses are conducted to demonstrate the usefulness and advantages of the proposed methodology.

An innovative Organic Rankine Cycle (ORC) based Ocean Thermal Energy Conversion (OTEC) system with performance simulation and multi-objective optimization

Based on multi-objective particle swarm optimization (MOPSO) algorithm, with considering levelized cost of energy (LCOE) and exergy efficiency as two different objective functions, an innovative Organic Rankine Cycle (ORC) model based Ocean Thermal Energy Conversion (OTEC) system is investigated for trade-off Pareto optimization. In the present study, six key parameters including evaporating temperature, condensing temperature, warm seawater temperature at the outlet of evaporator, cool seawater temperature at the outlet of condenser, degree of superheat, and depth of cool seawater have been selected as decision variables. R717, R152a, R134a, R227ea, R600a and R601 are chosen as working fluids. Meanwhile, Linear Programming Technique for Multi-dimensional Analysis of Preference (LINMAP) is introduced in order to make decision for Pareto frontier. The results indicate that LCOE and exergy efficiency are two conflicting objectives, which are impossible to both achieve their optimal values simultaneously. According to the non-dominated sorting of Pareto optimal solution (POS) for the six working fluids, R717 and R601 have the best performance with 0.34 $/kWh of LCOE, 28.17% of exergy efficiency and 0.52 $/kWh of LCOE, 28.47% of exergy efficiency, respectively, followed by R152a, R600a and R134a which have relatively poor performance, but better than R227ea.

Solving MCDM problems based on combination of PACMAN and LINMAP

AbstractMulticriteria decision‐making approaches are receiving more and more attention with the increase of expectations from decision makers in variety of fields. The growth in applying such approaches has led to identifying their strengths as well as their shortcomings. Passive and active compensability multicriteria analysis (PACMAN) is one of the frequently used approaches which has the capability to consider compensation in describing intercriteria relations in multicriteria decision‐making problems. This methodology is well formed and rationally structured in the first two phases, in which the problem is formulated and the decisive indices are obtained. However, it has some shortcomings in the idea of concluding the process of solution in its last phase. In the current study, we review the methodology, discuss its possible shortcomings, and propose an approach based on the combination of PACMAN and linear programming technique for multidimensional analysis of preference (LINMAP). The proposed approach which is taken to evaluate the PACMAN and LINMAP methodologies can help researchers and decision makers who seek an accurate perspective to evaluate a multicriteria decision‐making methodology.

Thermodynamic analysis and multi-objective optimisation of endoreversible Lenoir heat engine cycle based on the thermo-economic performance criterion

ABSTRACTA thermodynamic model of a steady-flow endoreversible Lenoir heat engine cycle (a ‘three-point’ cycle) coupled with constant-temperature heat reservoirs is established in this paper by using finite-time thermodynamic theory. The cycle consists of one isochoric heating branch, one adiabatic expansion branch and one isobaric cooling branch. A mathematical approach based on the finite-time thermodynamic is proposed to obtain thermal efficiency, the output power and the entropy generation rate throughout the Lenoir system. In this study, an irreversible Lenoir engine is analysed thermodynamically in order to optimise its performance. In this regard, the optimal values of the ecological coefficient of performance and dimensionless thermo-economic objective functions of the Lenoir heat engine are determined. Multi-objective evolutionary algorithms based on Non-dominated Sorting Genetic Algorithm II algorithm is applied to the aforementioned system for calculating the optimal values of decision variables. Decision variables considered in this paper include the ratio of fluid temperature (), the effectiveness of the cold-side heat exchanger, the effectiveness of the hot-side heat exchanger, the temperature of state 1 and relative investment cost parameter of the hot-side heat exchanger. Moreover, Pareto optimal frontier is applied and an ultimate optimal answer is chosen via three competent decision-making approaches comprising Linear Programming Technique for Multidimensional Analysis of Preference, fuzzy Bellman-Zadeh and Technique for Order of Preference by Similarity to Ideal Solution.

A Hybrid MCDM Approach for Large Group Green Supplier Selection With Uncertain Linguistic Information

With increasing global concerns toward environmental protection and sustainable development, green supply chain management (GSCM) has drawn much attention from academicians and practitioners. Selecting an optimal green supplier is a critical part of GSCM, which can be viewed as a kind of multi-criteria decision making (MCDM) problem. To derive the best result, a large group of decision makers are often involved in the green supplier selection nowadays. Besides, decision makers tend to express their evaluations utilizing uncertain linguistic terms due to the vagueness of human thinking. Hence, this paper aims to propose a hybrid MCDM approach for green supplier selection within the large group setting. More concretely, interval-valued intuitionistic uncertain linguistic sets are applied for assessing the performance of green suppliers concerning each criterion. Ant colony algorithm is utilized to cluster decision makers into several subgroups. The linear programming technique for multidimensional analysis of preference is adopted for the determination of the optimal weights of criteria objectively. Finally, an extended MULTIMOORA approach is utilized to generate the ranking of alternative suppliers. The practicality and usefulness of the developed large group green supplier selection framework is illustrated using an empirical example of a real estate company.

Root Traits Enhancing Rice Grain Yield under Alternate Wetting and Drying Condition.

Reducing water requirements and lowering environmental footprints require attention to minimize risks to food security. The present study was conducted with the aim to identify appropriate root traits enhancing rice grain yield under alternate wetting and drying conditions (AWD) and identify stable, high-yielding genotypes better suited to the AWD across variable ecosystems. Advanced breeding lines, popular rice varieties and drought-tolerant lines were evaluated in a series of 23 experiments conducted in the Philippines, India, Bangladesh, Nepal and Cambodia in 2015 and 2016. A large variation in grain yield under AWD conditions enabled the selection of high-yielding and stable genotypes across locations, seasons and years. Water savings of 5.7–23.4% were achieved without significant yield penalty across different ecosystems. The mean grain yield of genotypes across locations ranged from 3.5 to 5.6 t/ha and the mean environment grain yields ranged from 3.7 (Cambodia) to 6.6 (India) t/ha. The best-fitting Finlay-Wilkinson regression model identified eight stable genotypes with mean grain yield of more than 5.0 t/ha across locations. Multidimensional preference analysis represented the strong association of root traits (nodal root number, root dry weight at 22 and 30 days after transplanting) with grain yield. The genotype IR14L253 outperformed in terms of root traits and high mean grain yield across seasons and six locations. The 1.0 t/ha yield advantage of IR14L253 over the popular cultivar IR64 under AWD shall encourage farmers to cultivate IR14L253 and also adopt AWD. The results suggest an important role of root architectural traits in term of more number of nodal roots and root dry weight at 10–20 cm depth on 22–30 days after transplanting (DAT) in providing yield stability and preventing yield reduction under AWD compared to continuous flooded conditions. Genotypes possessing increased number of nodal roots provided higher yield over IR64 as well as no yield reduction under AWD compared to flooded irrigation. The identification of appropriate root architecture traits at specific depth and specific growth stage shall help breeding programs develop better rice varieties for AWD conditions.

Pythagorean Fuzzy LINMAP Method Based on the Entropy Theory for Railway Project Investment Decision Making

The uncertainty and complexity of the decision-making environment and the subjectivity of the decision makers will lead to the inevitable errors of the decision-making data. A poor decision will be produced with those errors, whereas the linear programming technique for multidimensional analysis of preference (LINMAP) method can adjust such errors through constructing an optimal programming model based on the consistency of the decision-making information, and it has been applied widely in multiple attribute group decision making (MAGDM). Moreover, Pythagorean fuzzy information is useful to simulate the ambiguous and uncertain decision-making environment. Therefore, the LINMAP method under the Pythagorean fuzzy circumstance will be proposed in this paper to solve MAGDM problems. To measure the fuzziness and uncertainty of Pythagorean fuzzy set (PFS) and interval-valued PFS, Pythagorean fuzzy entropy (PFE) and interval-valued PFE (IVPFE) grounded on the similarity and hesitancy parts have been defined, respectively. Then, Pythagorean fuzzy LINMAP (PF LINMAP) methods are constructed on the basis of the PFE and IVPFE correspondingly. Under the given preference relations, the maximum consistency and the amount of knowledge can be realized by the proposed methods. After investigating the relevant indicator system, the decision-making problem concerning railway project investment has been solved through the proposed PF LINMAP method with PFE. Finally, the practicability and effectiveness of the PF LINMAP method has been verified via the comparative analysis with the existing methods.